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What is the value of the leading coefficient a, if the polynomial function P(x) = a(x + b)2(x − c) has a multiplicity of 2 at the point (−1, 0) and also passes through the points (7, 0) and (0, −14)?

 

A:2

B:-2

C:7

D:-14

 

Thanks for the help :)

 Mar 13, 2018
 #1
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If we have a multiplicity of 2 at  (-1,0)  and the point (7,0) is also on the graph, we must have that

 

P(x) =

a (x + 1)^2 (x - 7)      

a (x^2 + 2x + 1) (x - 7)  

a(x^3 + 2x^2 + x -7x^2 -14x - 7)  

a(x^3 - 5x^2 - 13x - 7)  

 

And if   (0, -14)  is on the graph.....we have that

 

-14  = a ( 0^3 - 5(0)^2 - 13(0)  - 7)

-14 = -7a

a  = 2

 

Here's a graph : https://www.desmos.com/calculator/wbejrdzi2x

 

 

 

 

cool cool cool

 Mar 13, 2018

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